A PARTIAL POSITIVE SOLUTION TO A CONJECTURE OF RICCERI

作者：Garcia Pacheco Francisco J; Hill Justin R

来源：Topological Methods in Nonlinear Analysis, 2015, 46(1): 57-67.

DOI：10.12775/tmna.2015.037

• Anti-proximinal
• barrelled
• Ricceri

In this manuscript we introduce a new class of convex sets called quasi-absolutely convex and show that a Hausdorff locally convex topological vector space satisfies the weak anti-proximinal property if and only if every totally anti-proximinal quasi-absolutely convex subset is not rare. This improves results from [7] and provides a partial positive solution to a Ricceri's Conjectured posed in [9] with many applications to the theory of partial differential equations. We also study the intrinsic structure of totally anti-proximinal convex subsets proving, among other things, that the absolutely convex hull of a linearly bounded totally anti-proximinal convex set must be finitely open. Finally, a new characterization of barrelledness in terms of comparison of norms is provided.

• 出版日期2015-9